Past, present, and future of precision determinations of the QCD coupling from lattice QCD.

Non-perturbative scale-dependent renormalization problems are ubiquitous in lattice QCD as they enter many relevant phenomenological applications. They require solving non-perturbatively the renormalization group equations for the QCD parameters and matrix elements of interest in order to relate their non-perturbative determinations at low energy to their high-energy counterparts needed for phenomenology. Bridging the large energy separation between the hadronic and perturbative regimes of QCD, however, is a notoriously difficult task.

QCD Coupling from a Nonperturbative Determination of the Three-Flavor Λ Parameter.

We present a lattice determination of the Λ parameter in three-flavor QCD and the strong coupling at the Z pole mass. Computing the nonperturbative running of the coupling in the range from 0.2 to 70 GeV, and using experimental input values for the masses and decay constants of the pion and the kaon, we obtain Λ_{MS[over ¯]}^{(3)}=341(12)  MeV.

Determination of the QCD Λ Parameter and the Accuracy of Perturbation Theory at High Energies.

We discuss the determination of the strong coupling α_{MS[over ¯]}(m_{Z}) or, equivalently, the QCD Λ parameter. Its determination requires the use of perturbation theory in α_{s}(μ) in some scheme s and at some energy scale μ. The higher the scale μ, the more accurate perturbation theory becomes, owing to asymptotic freedom.